Working from the Sunny 16, it is four stops between f/4 and f/16:
Assuming an ISO of 100, 1/100th of a second to two minutes is 14 stops
- 1/100 - 1/60 - 1/30 - 1/15 - 1/8 - 1/4 - 1/2 - 1 second - 2 - 4 - 8 - 15 - 30 - 1 minute - 2 minutes.
Together, this will suggest you would need about 18 stops of density to get a 2 minute exposure at f/4 on a sunny day. You can reduce this by using a lower ISO (can your camera do ISO 50? 25?), using a faster exposure (1 minute? 30 seconds?) or stoping down a bit more from f/4 (if you don't need the shallower depth of field for f/4, why not f/11 or f/16?), but you'll still be in the high teens area of amount of density you will need.
Specfically for this application, you may wish to consider a pair of filters such as a variable ND which will give you between 2 and 8 stops and then either a 10 or 15 stop filter. Note that I've linked Singh-Ray which is a high end filter provider - you may be able to find a less expensive alternatives to the variable and solid ND providers (though Singh-Ray is the only 15 stop producer I've found). Take care you don't stack too much glass (the variND is rather thick) which can lead to some vignetting with wide shots.